Deleting vertices and interlacing of $A_\alpha$ eigenvalues of a graph
Received:September 06, 2021  Revised:November 18, 2021
Key Word: $A_{\alpha}$ eigenvalue, interlacing inequality, independence number, cover number, Hamiltonian properties, spanning tree.  
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Author NameAffiliationAddress
Hongzhang Chen School of Mathematics and Statistics, Minnan Normal University School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000
Jianxi Li School of Mathematics and Statistics, Minnan Normal University School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000
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Abstract:
      Let $G$ be simple graph with vertex set $V$ and edge set $E$. In this paper, we establish an interlacing inequality between the $A_{\alpha}$ eigenvalues of $G$ and its subgraph $G-U$, where $U\subseteq V$. Moreover, as an application, this interlacing property can be used to deduce some $A_{\alpha}$ spectral conditions concerning the independence number, cover number, Hamiltonian property and spanning tree of a graph, respectively.
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